Dirichlet-Multinomial Probability Distribution

See: Document Classification, Compound Probability Distribution, Dirichlet Distribution, Categorical Distribution, Beta-Binomial Distribution.

References

(Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/Dirichlet-multinomial_distribution Retrieved:2015-6-25.
- In probability and statistics, the Dirichlet-multinomial distribution is a probability distribution for a multivariate discrete random variable. It is also called the Dirichlet compound multinomial distribution (DCM) or multivariate Pólya distribution (after George Pólya). It is a compound probability distribution, where a probability vector p is drawn from a Dirichlet distribution with parameter vector [math]\displaystyle{ \boldsymbol{\alpha} }[/math] , and a set of discrete samples is drawn from the categorical distribution with probability vector p. The compounding corresponds to a Polya urn scheme. In document classification, for example, the distribution is used to represent the distributions of word counts for different document types.